PrologMethods/Regression/linear_regression.md

+# Simple Linear Regression and Prediction
+
+An implementation of simple linear regression and ridge regression using ordinary least squares.
+
+# Available Predicates
+
+* [initModel/7](/PrologMethods/Regression/linear_regression#initmodel7)
+* [initModelWithWeights/9](/PrologMethods/Regression/linear_regression#initmodelwithweights9)
+* [computeError/6](/PrologMethods/Regression/linear_regression#computeerror6)
+* [parameters/2](/PrologMethods/Regression/linear_regression#parameters2)
+* [modifyParameters/2](/PrologMethods/Regression/linear_regression#modifyparameters2)
+* [predict/5](/PrologMethods/Regression/linear_regression#predict5)
+* [train/7](/PrologMethods/Regression/linear_regression#train7)
+* [trainWithWeights/9](/PrologMethods/Regression/linear_regression#trainwithweights9)
+
+---
+
+[links/resources](/PrologMethods/Regression/linear_regression#connected-linksresources)
+
+## **_initModel/7_**
+
+Initializes the linear_regression model and trains it but doesnt include weights.
+
+```prolog
+%% part of the predicate definition
+initModel(  +pointer(float_array), +integer, +integer, 
+            +pointer(float_array), +integer, 
+            +float32, 
+            +integer).
+```
+
+### Parameters
+| Name | Type | Description | Default |
+|------|------|-------------|---------|
+| data | +matrix | X, matrix of data points. | - |
+| responses | +vector | y, the measured data for each point in X. | - |
+| lambda | +float | Regularization constant for ridge regression. | 0.0 |
+| intercept | +integer(bool) | Whether or not to include an intercept term. | (1)true |
+
+---
+
+## **_initModelWithWeights/9_**
+
+Initializes the linear_regression model, trains it and adds weights to it.
+
+```prolog
+%% part of the predicate definition
+initModelWithWeights(  +pointer(float_array), +integer, +integer, 
+                       +pointer(float_array), +integer, 
+                       +pointer(float_array), +integer, 
+                       +float32, 
+                       +integer).
+```
+
+### Parameters
+| Name | Type | Description | Default |
+|------|------|-------------|---------|
+| data | +matrix | X, matrix of data points. | - |
+| responses | +vector | y, the measured data for each point in X. | - |
+| weights | +vector | Observation weights (for boosting). | - |
+| lambda | +float | Regularization constant for ridge regression. | 0.0 |
+| intercept | +integer(bool) | Whether or not to include an intercept term. | (1)true |
+
+---
+
+## **_computeError/6_**
+
+Calculate the L2 squared error on the given predictors and responses using this linear regression model.
+
+```prolog
+%% part of the predicate definition
+computeError(  +pointer(float_array), +integer, +integer, 
+               +pointer(float_array), +integer, 
+               [-float32]).
+```
+
+### Parameters
+| Name | Type | Description | Default |
+|------|------|-------------|---------|
+| points | +matrix | Matrix of predictors (X). | - |
+| responses | +vector | Transposed vector of responses (y^T). | - |
+| error | -float | As this number decreases to 0, the linear regression fit is better. | - |
+
+---
+
+## **_parameters/2_**
+
+Get the parameters (the b vector).
+
+```prolog
+%% part of the predicate definition
+parameters([-pointer(float_array)], -integer).
+```
+
+### Parameters
+| Name | Type | Description | Default |
+|------|------|-------------|---------|
+| parameters | -vector | Get the parameters (the b vector). | - |
+
+---
+
+## **_modifyParameters/2_**
+
+Modify the parameters (the b vector).
+
+```prolog
+%% part of the predicate definition
+modifyParameters(+pointer(float_array), +integer).
+```
+
+### Parameters
+| Name | Type | Description | Default |
+|------|------|-------------|---------|
+| newParameters | +vector | Modify the parameters (the b vector). | - |
+
+---
+
+## **_predict/5_**
+
+Calculate y_i for each data point in points.
+
+```prolog
+%% part of the predicate definition
+predict(  +pointer(float_array), +integer, +integer, 
+          -pointer(float_array), -integer).
+```
+
+### Parameters
+| Name | Type | Description | Default |
+|------|------|-------------|---------|
+| points | +matrix | the data points to calculate with. | - |
+| predictions | -vector | y, will contain calculated values on completion. | - |
+
+---
+
+## **_train/7_**
+
+Train the linear_regression model on the given data.
+
+Careful! This will completely ignore and overwrite the existing model. This particular implementation does not have an incremental training algorithm.
+
+```prolog
+%% part of the predicate definition
+train(  +pointer(float_array), +integer, +integer, 
+        +pointer(float_array), +integer, 
+        +integer, 
+        [-float32]).
+```
+
+### Parameters
+| Name | Type | Description | Default |
+|------|------|-------------|---------|
+| data | +matrix | X, matrix of data points. | - |
+| responses | +vector | y, the measured data for each point in X. | - |
+| intercept | +integer(bool) | Whether or not to include an intercept term. | (1)true |
+| error | -float | The least quares error after training. | - |
+
+---
+
+## **_trainWithWeights/9_**
+
+Train the linear_regression model on the given data and weights.
+
+Careful! This will completely ignore and overwrite the existing model. This particular implementation does not have an incremental training algorithm.
+
+```prolog
+%% part of the predicate definition
+trainWithWeights(  +pointer(float_array), +integer, +integer, 
+                   +pointer(float_array), +integer, 
+                   +pointer(float_array), +integer, 
+                   +integer, 
+                   [-float32]).
+```
+
+### Parameters
+| Name | Type | Description | Default |
+|------|------|-------------|---------|
+| data | +matrix | X, matrix of data points. | - |
+| responses | +vector | y, the measured data for each point in X. | - |
+| weights | +vector | Observation weights (for boosting). | - |
+| intercept | +integer(bool) | Whether or not to include an intercept term. | (1)true |
+| error | -float | The least quares error after training. | - |
+
+---
+
+# Connected Links/Resources
+
+If you want a more detailed explanation, then go to the python documentation. There is most of the time a good explanation on how the methods work and what the parameters do.
+
+* [MLpack::linear_regression_C++\_documentation](https://www.mlpack.org/doc/stable/doxygen/classmlpack_1_1regression_1_1LinearRegression.html)
+* [MLpack::linear_regression_Python_documentation](https://www.mlpack.org/doc/stable/python_documentation.html#linear_regression)
+
+added some of the links from the python documentation
+
+* [lars](https://gitlab.cs.uni-duesseldorf.de/stups/abschlussarbeiten/prolog-mlpack-libary/-/wikis/PrologMethods/Regression/lars)
+* [Linear regression on Wikipedia](https://en.wikipedia.org/wiki/Linear_regression)
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